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CAT 1996 | Question: 122

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A salesman enters the quantity sold and the price into the computer. Both the numbers are two-digit numbers. Once, by mistake, both the numbers were entered with their digits interchanged. The total sales value remained the same, i.e. Rs. $1148$, but the inventory reduced by $54$.

What is the actual quantity sold?

  1. 28
  2. 14
  3. 82
  4. 41
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Since the total sales value remained the same in spite of entering with their digits interchanged, both its digits must've been the same.

But the inventory reduced by 54.

Suppose the number to be entered was xy = 10x + y which was mistakenly entered to be yx = 10y + x

So,

xy - yx = 54

10x + y - (10y + x) = 54

9x - 9y = 54

$\therefore$ x - y = 6 ...

From the given options, only C satisfies the above equation.

C is the answer.

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